Tuesday, February 26, 2008

Three Kepler Laws

Kepler had predicted that with Tycho’s data, he would solve the problem of planetary motion in a matter of days. After almost eight years of study, trial, and error, Kepler had a stroke of genius. He concluded that the planets must orbit the sun not in perfect circles, but in elliptical orbits (an ellipse is a flattened circle). He wrote to a friend: “I have the answer … The orbit of the planet is a perfect ellipse. Kepler was able to state the fundamentals of planetary motion in three basic laws.

That planets move in elliptical orbits, with the sun at one focus of the ellipse, is known as Kepler’s First Law. It resolved the discrepancies in observed planetary motion that both Ptolemy and Copernicus had failed to explain adequately. Both of those great minds had been convinced that in a perfect universe, the orbits of planets had to be circular.

Another apparent attribute of elliptical orbits determined Kepler’s Second Law. It states that an imaginary line connecting the sun to any planet would sweep out equal areas of the ellipse in equal intervals of time. The Second Law explained the variation in speed with which planets travel. They will move faster when they are closer to the sun. Kepler did not say why this was so, just that it was apparently so. Later minds would confront that why. The first two of Kepler’s laws were published in 1609.

The third did not appear until ten years later and is slightly more complex. It states that the square of a planet’s orbital period (the time needed to complete one orbit around the sun) is proportional to the cube of its semi-major axis. Since the planets’ orbits, while elliptical, are very nearly circular, the semi-major axis can be considered to be a planet’s average distance from the sun.